A367475 Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^3.

1, 6, 54, 636, 9204, 157584, 3111312, 69533472, 1734229344, 47733263232, 1436801816448, 46942939272960, 1654215709835520, 62533593070755840, 2524077593084160000, 108339176213529384960, 4927173048408858531840, 236673892535088351744000

Offset: 0

Author

Seiichi Manyama, Nov 19 2023

Keywords

• nonn

Crossrefs

Cf. A088500, A367474.

Cf. A354122, A367471.

Programs

Maple

A367475 := proc(n)
    option remember ;
    if n =0 then
        1;
    else
        2*add((2*k/n + 1) * (k-1)! * binomial(n,k) * procname(n-k),k=1..n) ;
    end if;
end proc:
seq(A367475(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

PARI

a(n) = sum(k=0, n, 2^k*(k+2)!*abs(stirling(n, k, 1)))/2;

Formula

a(n) = (1/2) * Sum_{k=0..n} 2^k * (k+2)! * |Stirling1(n,k)|.

a(0) = 1; a(n) = 2*Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).